Bonjour!
Demain, à 10h30 en B107, Jad Koleilat nous parlera sur le sujet suivant.
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Cartesian Differential Categories are a categorical axiomatisation of
differentiation between vector spaces. A CDC is a cartesian category
equipped with a differential operator, associating to each morphism f :
A -> B a morphism Df : A x A -> B. The category of real finite
dimentional vector spaces and smooth function is an example of CDC.
Historically, they were discovered wile studying categorical models of a
certain logic called Differential Linear Logic (DiLL). Since 2021, we
know that there exists a strong duality between CDC and models of DiLL
: the coKleisli of every model of DiLL is a CDC and every CDC embeds
fully and faithfully into the coKleisli of a model of DiLL. This duality
can appear somewhat surprising as it is not often that such
logical/mathematical duality exists especially in the context of
non-discrete structures.
In this talk, I will explain what are CDC, what are models of DiLL, the
duality between them and try to convey the intuitions I have on those
structures.
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Il est possible que la réunion soit plus court que d'habitude.
Bien cordialement,
Morgan Rogers
